Back around 2014 a friend of mine was interested in playing Skyrim on a laptop with a 4th gen Core i5-4200u CPU and Intel HD 4400 with a 1080p screen and 8GB of RAM. I have a pretty similar laptop, but it also had a Radeon HD 8850m dedicated GPU. I already had Skyrim installed on that laptop so I disabled the Radeon HD 8850m to force Skyrim to use the Intel HD 4400. I backed up the SkyrimPref.ini file before I stated to make a lot of edits.
The SkyrimPref.ini file has a lot of graphic settings that you cannot be changed in the game's graphics options. For example, the only way to disable shadows is to do it in the SkyrimPref.ini file. Disabling shadows can really improve performance, but I made a lot more edits than simply disabling shadows.
In the end, I tweaked Skyrim to the point where it ran at between 40 FPS and 50 FPS most of the time at 1600x900 resolution. Combat can cause FPS dip sometimes and FPS will drop outdoors when the game loads new map textures. I let him play Skyrim on my laptop to try it out. He was satisfied with the performance.
To disable shadows in the SkyrimPref.ini file you need to search for the display section labeled as [Display]. From there you should make the following changes which changes the distance of how far shadows will appear before they fade. Changing the values to 0 disables shadows.
Having 2 sticks of RAM instead of only 1 stick means the RAM will be running in dual channel mode (full speed) rather than single channel mode (half speed). This can improve game performance when using integrated graphics by around 10% to 20% depending on the game.